Expert: Scott A Wilson - 2/17/2009

Question
find the slope
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(-2,5) and (4,7)

through the origin and (11,-2)

2x + 3y = 15

y + 4 = 9

y= -3x
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find the equation in the form y = mx + b

through (5,-1); slope = 2/3
through (5,-2) and (1,3)
through (-1,4); undefined slope
through (2,-1), parrell to 3x - y = 1
through (2, -10), perperdicualr to a line with undifined slope
through (3,-5), parallel to y=4
through (-7,4), perpendicular to y=8
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The supply and demand for crabmeat in a local fish store and related by the equation:
supply: p = S(q) = 6q + 3
demand: p = D(q) = 19 - 2q
where p represents the price in dollars per pound and q represents the quantity of crabmeat in pounds per day. Find the supply and demand at each of the following prices.
a.$10  b.$15  c.$18

d. find the equilibrium price
e. find the equilibrium quantity.
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Cost. Find a linear cost function
1.Eight units cost $300; fixed cost is $60
2.12 units cost $445; 50 units cost $1585
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Breakeven analysis. The cost of producing x cartons of cd's is C(x)dollars , where C(x) = 200x + 1000. The cd's sell for $400 per carton.
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The U.S. is China's largest export market. Imports form china have grown from about 19 billion dollars in 1991 to 102 billion dollars in 2001. This growth has been approximately linear. Use the given data pairs to write a linear equation that describes this growth in imports over the years. Let x=91 and x=101
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Answer
find the slope - the slope of this is (y2-y1)/(x2-x1)
where (x1,y1) and (x2,y2) are the two points (-2,5) and (4,7).

Through the origin, take (-2,5) and (0,0) for the first.
Take (4,7) and (0,0) for the next.

Through (11,-2), do the same as the last problem, replacing
the origin { (0,0) } with (11,-2).

Convert the following to the form y = mx + b.
The slope of each of them would be m.
To convert them, subtract off anything that's not y on the left side
from both sides, then divide by the number in front y.

2x + 3y = 15

y + 4 = 9

y= -3x
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find the equation in the form y = mx + b

through (5,-1); slope = 2/3
y-y1 = m(x-x1) m = 2/3; x1=5; y1=-5

through (5,-2) and (1,3)
m=(y2-y1)/(x2-x1); y=m(x-x1) + y1; (x1,y1)=(5,-2), (x2,y2)=(1,3)

through (-1,4); undefined slope
can't find one

through (2,-1), parrell to 3x - y = 1
(x1,y1) = (2,-1); m = -1; y = m(x-x1) + y1

through (2, -10), perperdicualr to a line with undefined slope
can't find this one either

through (3,-5), parallel to y=4
slope is 0, so y=-5 is paralell and through the point indicated

through (-7,4), perpendicular to y=8
x=-7 is the straight up and down line that is perpendicular to
the line y = 8 { a horzontal line }.
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The supply and demand for crabmeat in a local fish store and related by the equation:
supply: p = S(q) = 6q + 3
demand: p = D(q) = 19 - 2q
where p represents the price in dollars per pound and q represents the quantity of crabmeat in pounds per day. Find the supply and demand at each of the following prices.
a.$10  b.$15  c.$18
Put 10, 15, and 18 in for p and solve for q in both equations.

d. find the equilibrium price
The equilibrium price can be found when supply = demand.
Set the two equation equal and solve for q.
Once this has been done, you can get p from either equation.

e. find the equilibrium quantity.
Didn't we just do that?
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Cost. Find a linear cost function
1.Eight units cost $300; fixed cost is $60
If the fixed is 60, then the price due to each product is 300-60=B.
Once this number has been found,
divide by 8 to get how much for each, C.
The equation is P = Cx + B.

2. 12 units cost $445; 50 units cost $1585
Take (1,585-445)/(50-12), and this will tell you the slope m.
Take y = mx + b and input (12,445) for (x,y) and
m from the last line.  Solve for b.
There's the equation.

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Breakeven analysis. The cost of producing x cartons of cd's is C(x)dollars , where C(x) = 200x + 1000. The cd's sell for $400 per carton.
Cost = 200x+1000
Return = 400x
Profit = Revenue - Cost = 200x + 1000

I don't see where this function can be maximized the way it is.
The more CD's that are produced, the greater profit there will be.
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The U.S. is China's largest export market. Imports form china have grown from about 19 billion dollars in 1991 to 102 billion dollars in 2001. This growth has been approximately linear. Use the given data pairs to write a linear equation that describes this growth in imports over the years. Let x=91 and x=101

Take y-y1=m(x-x1) where (x1,y1)=(91,102) and (x2,y2)=(101,102).
m is found as (y2-y1)/(x2-x1).

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